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The formation of a layered structure when a stable salinity gradient is heated from below

Published online by Cambridge University Press:  21 April 2006

Harindra J. S. Fernando
Harindra J. S. Fernando
Affiliation:
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287, USA
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Abstract

It is well known that heating a stable salinity gradient from below leads to the formation of a series of turbulently convecting layers separated by stable diffusive interfaces. It is argued theoretically and demonstrated experimentally that the first mixed layer grows to a critical height δc, which is determined by a balance between the vertical kinetic and potential energies of the turbulent eddies, before a growing second layer separated from the first layer by a quasi-stationary stable density interface can be formed. Although the thermal boundary layer that develops over the propagating turbulent front can become unstable and form a second mixed region before the first layer grows to δc, the density interface formed between these two layers is not sufficiently stable to resist quick entrainment of the second layer into the lower layer. Some aspects of the growth of the first turbulent layer and possible application of the results to oceanic situations are also discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 182 , September 1987 , pp. 525 - 541
Copyright
© 1987 Cambridge University Press

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References

Carruthers, D. J. & Hunt, J. C. R. 1986 Velocity fluctuations near an interface between a turbulent region and a stably stratified layer. J. Fluid Mech. 165, 475–501.Google Scholar
Chen, C. F., Briggs, D. G. & Wirtz, R. A. 1971 Stability of thermal convection in a salinity gradient due to lateral heating. Intl J. Heat & Mass Transfer 14, 57–65.Google Scholar
Crapper, P. F. & Linden, P. F. 1974 The structure of the turbulent density interfaces. J. Fluid Mech. 65, 45–63.Google Scholar
Currie, I. G. 1967 The effect of heating rate on the stability of stationary fluids. J. Fluid Mech. 29, 339–347.Google Scholar
Deardorff, J. W., Willis, G. E. & Stockton, B. H. 1980 Laboratory studies of the entrainment zone of a convective mixed layer. J. Fluid Mech. 100, 41–64.Google Scholar
Federov, K. N. 1970 On the step-like structure of temperature inversions in the ocean. Izv. Atmos. Ocean Phys. 6, 1178–1188.Google Scholar
Fernando, H. J. S. 1987a On the growth of a turbulent patch in a stratified fluid. J. Fluid Mech. (submitted).Google Scholar
Fernando, H. J. S. 1987b Buoyancy transfer across a diffusive interface separated by two convecting layers. J. Fluid Mech. (submitted).Google Scholar
Fernando, H. J. S. & Long, R. R. 1983 The growth of a grid-generated mixed layer in a two-fluid system. J. Fluid Mech. 133, 377–395.Google Scholar
Fernando, H. J. S. & Long, R. R. 1985a On the nature of the entrainment interface of a two-layer fluid subjected to zero-mean-shear turbulence. J. Fluid Mech. 151, 21–53.Google Scholar
Fernando, H. J. S. & Long, R. R. 1985b The deepening of a mixed layer in a linearly stratified fluid. Phys. Fluids 28, 2999–3005.Google Scholar
Gregg, M. C. 1984 Persistent turbulent mixing and near-inertial waves. In Internal Gravity Waves and Small Scale Turbulence (ed. P. Muller & R. Pujalet), pp. 1–24. Hawaii Institute of Geophysics, Special Publication.
Hannoun, I. A., Fernando, H. J. S. & List, E. J. 1987 Turbulence structure near a sharp density interface. J. Fluid Mech. (in press).Google Scholar
Hoare, R. A. 1966 Problem of heat transfer in Lake Vanda, a density stratified arctic lake. Nature 210, 787–789.Google Scholar
Howard, L. N. 1964 Convection at high Rayleigh numbers. In Proc. 11th Intl Congress of Applied Mechanics, Munich (ed. H. Görtler). Springer.
Hunt, J. C. R. 1984 Turbulence structure in thermal convection and shear-free boundary layers J. Fluid Mech. 138, 161–184.Google Scholar
Huppert, H. E. & Linden, P. F. 1979 On heating a stable salinity gradient from below. J. Fluic Mech. 95, 431–464.Google Scholar
Incropera, F. P. & DeWitt, D. P. 1985 Fundamentals of Heat and Mass Transfer. Wiley.
Krause, G. 1968 Struktur und Verteilung des Wassers aus dem Roten Meer im Nordwesten des Indischen Ozeans. ‘Meteor’ Forschungsergebnisse A, Heft 4.
Linbaugh, C. & Rechnitzer, A B. 1955 Visual detection of temperature—density discontinuities in water by dividing. Science 121, 395.Google Scholar
Linden, P. F. 1973 The interaction of vortex rings with a sharp density interface: a model for turbulent entrainment. J. Fluid Mech. 60, 467–480.Google Scholar
Linden, P. F. 1975 The deepening of a mixed layer in a linearly stratified fluid. J. Fluid Mech 71, 385–405.Google Scholar
Long, R. R. 1978 A theory of mixing in a stably stratified fluid. J. Fluid Mech. 84, 113–124.Google Scholar
Lubimova, E. A., Richard, P., Von Herzen, R. P. & Udintzev, G. B. 1965 On heat transfer through the ocean floor. Terrestrial Heat Flow. Geophys. Monograph, vol. 8, p. 78.Google Scholar
Mack, S. 1985 Two-dimensional measurement of oceanic microstructure: the role of double diffusion. J. Phys. Oceanogr. 15, 1581–1604.Google Scholar
Narimousa, S. & Fernando, H. J. S. 1987 On the sheared density interface of an entraining stratified fluid. J. Fluid Mech. 174, 1–22.Google Scholar
Newman, F. C. 1976 Temperature steps in Lake Kivu: a bottom heated saline lake. J. Phys Oceanogr. 6, 157–163.Google Scholar
Oster, G. & Yamamoto, M. 1963 Density gradient techniques. Chem. Rev. 63, 257.Google Scholar
Schmitt, R. W. 1981 Form of the temperature—salient relationship in the central water: evidence of double diffusive mixing. J. Phys. Oceanogr. 11, 1015–1026.Google Scholar
Shirtcliffe, T. G. L. & Calhaem, I. M. 1968 Measurements of temperature and electrical conductivity in Lake Vanda, Victoria Land, Antarctica. New Zealand. J. Geol. Geophys. 11, 976–981.Google Scholar
Siedler, G. 1968 Schichtungs- und Bewegungsverhältnisse am Südausgang des Roten Meeres ‘Meteor’ Forschungsergebnisse A, Heft 4.
Stegan, G. R., Hendricks, P. J. & Muench, R. D. 1985 Vertical mixing on the Bering Sea sheft In The Ocean Surface: Wave Breaking, Turbulent Mixing and Radio Probing (ed. Y. Toba & H. Mitsuyasu), pp. 553–558. Reidel.
Swallow, J. C. & Crease, J. 1965 Hot salty water at the bottom of the Red Sea. Nature 205, 165–166.Google Scholar
Thorpe, S. A. 1977 Turbulence and mixing in a Scottish loch. Phil. Trans. R. Soc. Lond. A 86, 125–181.Google Scholar
Turner, J. S. 1968 The behaviour of a salinity gradient heated from below. J. Fluid Mech. 33, 183–200.Google Scholar
Turner, J. S. & Stommel, H. 1964 A new case of convection in the presence of vertical salinity and temperature gradients. Proc. Natl Acad. Sci. 52, 49–53.Google Scholar
Veronis, G. 1965 On finite amplitude instability in thermohaline convection. J. Mar. Res. 23, 1–17.Google Scholar
Woods, J. D. 1968 Wave induced shear instability in the summer thermocline. J. Fluid Mech. 32, 791–800.Google Scholar